Question

1. (1’) The position function of a particle is given by s(t) =
3t2 − t3, t ≥ 0.

(a) When does the particle reach a velocity of 0 m/s? Explain the
significance of this value of t.

(b) When does the particle have acceleration 0 m/s2?

2. (1’) Evaluate the limit, if it exists.

lim |x|/x→0 x

3. (1’) Use implicit differentiation to find an equation of the tangent line to the curve sin(x) + cos(y) = 1

at the point (π, π).

Answer #1

The velocity function of a particle is given by v(t) = 3t2 – 24t
+ 36.
a) Find the equation for a(t), the acceleration.
b) If s(1) = 50, find the displacement function s(t).
c) When will the velocity be zero?
d) Find the distance the particle travels on [0, 4].

The position of a particle is given in cm by x = (2) cos 9?t,
where t is in seconds.
(a) Find the maximum speed.
0.565 m/s
(b) Find the maximum acceleration of the particle.
_______m/s2
(c) What is the first time that the particle is at x = 0 and
moving in the +x direction?
_______s

1) The position of a particle moving along x direction is given
by: x=8t-3t2.What is the velocity of the particle at t=2
s and what is the acceleration?
2) A roller coaster car starts from rest and descends
h1= 40 m. The car has a mass of 75 kg. What is the speed
at 20m while going down the hill?

Find the velocity, acceleration, and speed of a particle with
the given position function.
(a) r(t) = e^t cos(t)i+e^t
sin(t)j+ te^tk, t = 0
(b) r(t) = 〈t^5 ,sin(t)+ t ^ cos(t),cos(t)+ t^2 sin(t)〉, t =
1

The function s(t) describes the position of a particle moving
along a coordinate line, where s is in feet and t is in
seconds.
s(t) = 3t2 - 6t +3
A) Find the anti-derivative of the velocity function and
acceleration function in order to determine the position function.
To find the constant after integration use the fact that
s(0)=1.
B) Find when the particle is speeding up and slowing down.
C) Find the total distance from time 0 to time...

Suppose the position of a particle is given
s(t)=(1/3)t3 - t2 - 8t + 10. Determine the
following
A) What is the velocity function v(t)=
B) What is the acceleration function a(t)=
C) What is the object at rest t=
D) What is the position of the object at rest? Be sure to enter
your answer as an exact fraction s=

The position of a particle is given in cm by x = (2)
cos 6πt, where t is in seconds.
(a) Find the maximum speed.
m/s
(b) Find the maximum acceleration of the particle.
m/s2
(c) What is the first time that the particle is at x = 0
and moving in the +x direction?
s

The position of a particle is given in cm by x = (9)
cos 5πt, where t is in seconds.
(a) Find the maximum speed.
.... m/s
(b) Find the maximum acceleration of the particle.
.... m/s2
(c) What is the first time that the particle is at x = 0
and moving in the +x direction?
..... s

A particle is moving with the given data. Find the position of
the particle. a(t) = 14 sin(t) + 3 cos(t), s(0) = 0, s(2π) = 18
s(t) =

A particle is moving with the given data. Find the position of
the particle.
a(t) = 18 sin(t) + 7 cos(t), s(0) =
0, s(2π) = 12
s(t)=

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